An example of an asymptotically Hilbertian space which fails the approximation property Academic Article uri icon

abstract

  • Following Davic's example of a Danach space failing the approximation property (1973), we show how to construct a Danach space E which is asymptotically Hilbcrtian and fails the approximation property. Moreover, the space E is shown to be a subspace of a space with an unconditional basis which is "almost" a weak Hubert space and which can be written as the direct sum of two subspaces all of whose subspaccs have the approximation property. © 2001 P. G. Casazza, C. L. Garcia, and W. B. Johnson.

author list (cited authors)

  • Casazza, P. G., Garca, C. L., & Johnson, W. B.

citation count

  • 6

complete list of authors

  • Casazza, PG||García, CL||Johnson, WB

publication date

  • April 2001